TheblockmodelfortheGriffithsphase吴新天1.ExperimetalevidenceofGriffithsphase2.Therenormalizationgroupforthephasetransition indisordered systems(a)Replicatrick.(b)Replicasymmetrybreaking3.The solutions of thesaddlepoint equation of Landau-GinzburgHamitonianwith randomtemperature.(a)Blockmodelforising-typesystems(b)Themethodtofindelementaryblocksandthecouplingsbetweenblocks.4.Theapplicationofblockmodel.(a)UniversalityviolationinBlume-Capelmodelwithrandombonds(b)Thepseudogapinstronglydisorderedconventionalsuperconductors.5.Summary
The block model for the Griffiths phase 2.The renormalization group for the phase transition in disordered systems (a) Replica trick. (b) Replica symmetry breaking. 3.The solutions of the saddle point equation of Landau-Ginzburg Hamitonian with random temperature. (a)Block model for ising-type systems. (b)The method to find elementary blocks and the couplings between blocks . 4.The application of block model. (a)Universality violation in Blume-Capel model with random bonds. (b)The pseudogap in strongly disordered conventional superconductors. 1. Experimetal evidence of Griffiths phase. 5.Summary. 吴新天
GriffithsPhaseR.B.Griffiths,Phys.Rev. Lett.23, 17 (1969)A.J.Bray,Phys.Rev.Lett.59,586(1987)TParamagneticT.oGriffithsregionx(h) is singularFerromagneticat h=00Pe-"compact"clusterofoccupiedsitesThe probabilityof these rare regions are proportionaltoIdTheGriffithssingularitiesare= exp(-Ld ln p)&pprobablyunobservable inexperiments
Griffiths Phase "compact" cluster of occupied sites R. B. Griffiths, Phys. Rev. Lett. 23, 17 (1969). A. J. Bray, Phys. Rev. Lett. 59, 586 (1987). p exp( L ln p) L d d = − − The probability of these rare regions are proportional to (h) is singular at h = 0 The Griffiths singularities are probably unobservable in experiments. ?
Roton at thetemperature above thesuperfluid transition25Tc=0.725K.Specifically.we observea well-HeinGeltech105%definedroton peak attemperature T>Tc in20Q-1.95AGeltechwhereas-observedinatorsionalT=35mKoscillatorexperiment.Sincetheexistenceof15well-defined excitations at higher wave1.3K(0FORvectorsabovethephonon(sound)regionT-1.5K10depends ontheexistenceof a Bose-Einsteincondensate (BEC),the observation of a well-definedrotonpeakabove TcsuggeststhatthereisBosecondensationaboveTcinGeltech.Dynamicstructurefactorofliquid4HeinGeltechlattherotonwavevectorattemperatures as shown.O.Plantevin,etal,Phys.Rev.B,65(2002)224505
O. Plantevin, et al, Phys. Rev. B, 65 (2002) 224505. Dynamic structure factor of liquid 4He in Geltechl at the roton wave vector at temperatures as shown. Roton at the temperature above the superfluid transition Tc=0.725 K. Specifically, we observe a welldefined roton peak at temperature T>Tc in Geltech where as observed in a torsional oscillator experiment. Since the existence of well-defined excitations at higher wave vectors above the phonon (sound) region depends on the existence of a Bose–Einstein condensate (BEC), the observation of a welldefined roton peak above Tc suggests that there is Bose condensation above Tc in Geltech. s = 0
Observation of a Griffiths Phase in Paramagnetic Lai-rSr,MnO175KPMsignalatg=2180KThisphaseis characterized bythe185Kcoexistenceofferromagneticentitieswithin(eethegloballyparamagneticphasefarabove190K200Kthemagnetic ordering temperature.30T=205KTc=175K,belowwhichthelongrangeT=253KorderexistsFMRsignal(suni)X=0.125210230250T(K)FMR:FerromagneticResonance5010Magneticfield (kOe)J.Deisenhofer, et.al, Phys.Rev. Lett. 95, 257202 (2005)
This phase is characterized by the coexistence of ferromagnetic entities within the globally paramagnetic phase far above the magnetic ordering temperature. Tc=175K, below which the long range order exists. FMR: Ferromagnetic Resonance. J. Deisenhofer, et. al, Phys. Rev. Lett. 95, 257202 (2005)
Griffithssingularitiesand magnetoresistivemanganites3x105DeviationfromtheusualCurie-Weisslaw.2x105() ()W/(0)WH1x105LCMO.Griths,LCMOLPMOGrifiths,LPMOLSMOoCurleLaw,S=1.850.91.01.11.21.31.41.5TITCTABLEI Transition temperatures and critical exponentsforsamplesstudied.β8Tc (scaling)Te(heatcapacity)Anomalous critical exponentsLCMO218K0.1016.9216.2K7.1LPMO286K285.1K0.245.1LSMO360K359.1K0.31MBSalamonandSHChun,Phys.Rev.B,68,014411(2003)
Griffiths singularities and magnetoresistive manganites Deviation from the usual Curie-Weiss law. Anomalous critical exponents. M B Salamon and S H Chun, Phys. Rev. B, 68, 014411 (2003)